Details

sample452.0ms

Algorithm

intervals

Results

94.0ms	91×	body	1280	valid
32.0ms	48×	body	640	valid
13.0ms	85×	body	80	valid
10.0ms	23×	body	320	valid
3.0ms	9×	body	160	valid

simplify47.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize16.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.3b	(/ (sin b) (cos (+ a b)))
3.6b	(cos (+ a b))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`associate-l` `associate-/r` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`cos-sum` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

3 → 67

Calls

3 calls:

27.0ms	(* r (/ (sin b) (cos (+ a b))))
17.0ms	(/ (sin b) (cos (+ a b)))
20.0ms	(cos (+ a b))

series255.0ms

Counts

3 → 9

Calls

3 calls:

145.0ms	(* r (/ (sin b) (cos (+ a b))))
78.0ms	(/ (sin b) (cos (+ a b)))
31.0ms	(cos (+ a b))

simplify1.5s

Counts: 76 → 76

prune330.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.1b	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b	(* (sin a) (sin b))
0.3b	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-r`
19×	`times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
3×	`flip3--` `prod-exp` `associate-/r` `frac-sub` `flip--` `cbrt-unprod` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`sub-neg` `frac-2neg` `diff-log` `associate-*r/` `clear-num`

Counts

4 → 100

Calls

4 calls:

19.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
87.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
19.0ms	(* (sin a) (sin b))
29.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series788.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
428.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
70.0ms	(* (sin a) (sin b))
185.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify817.0ms

Counts: 112 → 112

prune594.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.1b	(* r (sin b))
0.2b	(* (sin a) (sin b))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`sin-mult`
4×	`associate-/r/` `cos-mult`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `diff-log` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 76

Calls

4 calls:

23.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
10.0ms	(* r (sin b))
13.0ms	(* (sin a) (sin b))
58.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series580.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
64.0ms	(* r (sin b))
83.0ms	(* (sin a) (sin b))
316.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify853.0ms

Counts: 88 → 88

prune489.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ 1 (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (* r (sin b))))
0.2b	(* (sin a) (sin b))
0.3b	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (* r (sin b)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
34×	`add-exp-log`
30×	`add-sqr-sqrt`
26×	`add-cube-cbrt` `*-un-lft-identity`
22×	`add-cbrt-cube`
14×	`div-exp`
9×	`pow1`
8×	`associate-/r*`
7×	`cbrt-undiv`
6×	`associate-r` `associate-l` `prod-exp` `div-inv` `associate-/l*`
4×	`cbrt-unprod` `associate-/l/` `add-log-exp`
3×	`rec-exp` `1-exp` `sin-mult`
2×	`frac-2neg` `pow-prod-down` `clear-num` `cos-mult` `*-commutative` `unswap-sqr`
1×	`flip3--` `pow-flip` `div-sub` `associate-/r/` `frac-sub` `flip--` `inv-pow` `sub-div`

Counts

4 → 119

Calls

4 calls:

17.0ms	(* r (sin b))
28.0ms	(/ 1 (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (* r (sin b))))
26.0ms	(* (sin a) (sin b))
53.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (* r (sin b)))

series859.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* r (sin b))
443.0ms	(/ 1 (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (* r (sin b))))
65.0ms	(* (sin a) (sin b))
279.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (* r (sin b)))

simplify1.1s

Counts: 131 → 131

prune562.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes271.0ms

Accuracy

56.3% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify1.1s

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.6s	2859×	body	1280	valid
1.5s	1880×	body	640	valid
354.0ms	2131×	body	80	valid
238.0ms	752×	body	320	valid
83.0ms	380×	body	160	valid